Is the center of the supergiant star a white dwarf?

According to An Introduction to Modern Astrophysics, there is a sentence in the book that describes a white dwarf at the center of a supergiant star.

As far as I know, in the case of a heavy star, the core of the heavy star is just an iron core, and if it collapses beyond the degenerative pressure, the core becomes a neutron star.

So, Is it correct to describe the center of a supergiant as a white dwarf?